Howdy,
Them looks like some automotive type, coil-over shocks

I had the same idea

...& "ran" into this same type of an issue, while building a kart (~20 years ago)
I agree, moving the lower shock mounts closer to the axle will help

but,
I think that you may need to pre-load them shocks a bit too
but then,
You'll probably need to add some "stops"
...so, the frame doesn't "arch" when you (unload it) get off or out of it
* I pre-loaded the shocks, on the kart I was building, by continually adjusting the upper shock mount downwards
...& "testing" (just setting in it, until the frame stayed nice-n-straight & level)